The aim of this paper is to characterize the radial structure of the star formation rate (SFR) in galaxies in the nearby Universe as represented by the CALIFA survey. The sample under study contains 416 galaxies observed with IFS, covering a wide range of Hubble types and stellar masses. Spectral synthesis techniques are applied to obtain radial profiles of the intensity of the star formation rate in the recent past, and the local sSFR. To emphasize the behavior of these properties for galaxies that are on and off the main sequence of star formation (MSSF) we stack the individual radial profiles in bins of galaxy morphology and stellar masses. Our main results are: a) The intensity of SFR shows declining profiles that exhibit very little differences between spirals. The dispersion between the profiles is significantly smaller in late type spirals. This confirms that the MSSF is a sequence of galaxies with nearly constant intensity of SFR b) sSFR values scale with Hubble type and increase radially outwards, with a steeper slope in the inner 1 HLR. This behavior suggests that galaxies are quenched inside-out, and that this process is faster in the central, bulge-dominated part than in the disks. c) As a whole, and at all radii, E and S0 are off the MSSF. d) Applying the volume-corrections for the CALIFA sample, we obtain a density of star formation in the local Universe of 0.0105 Msun/yr/Mpc^{-3}. Most of the star formation is occurring in the disks of spirals. e) The volume averaged birthrate parameter, b=0.39, suggests that the present day Universe is forming stars at 1/3 of its past average rate. E, S0, and the bulge of early type spirals contribute little to the recent SFR of the Universe, which is dominated by the disks of later spirals. f) There is a tight relation between the intensity of the SFR and stellar mass, defining a local MSSF relation with a logarithmic slope of 0.8.
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